The failure criteria of anisotropic materials, the criteria being expressed via deformations, are rarely applied in practice, and are usually used for low-ductility materials. Another situation involves the simulation of failures in materials with the high anisotropy of mechanical properties and that suffer elastic-brittle fracture. For such materials the failure criteria are formulated using ultimate strains and strain tensor invariants. For simulating the fractures of materials that are characterized by the anisotropy of strength properties, the failure criteria are applied with the critical values of stresses and strains, as well as their intensities. Using the value of cumulative plastic strain as a failure criterion does reflect the anisotropy of elastic and plastic properties of a material, but it does not reflect that of the strength properties. The application of this method allows accounting the total plastic strain induced by tension and compression in the conditions of the wave strain of target...